Finite Group Databasebeta

← #13369366

Subgroups — #13369366

Order 1792.

1446 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×D4×Q8C211yesmaximal, characteristic
2C2×#89997C211yesmaximal, characteristic, complemented
3C22×#6409C211yesmaximal, characteristic, complemented
4#11739780C211yesmaximal, characteristic
5C2×#89783C211yesmaximal, characteristic
6#11729886C211yesmaximal, characteristic, complemented
7#11729886C211yesmaximal, characteristic, complemented
8#11729540C211yesmaximal, characteristic, complemented
9#11729532C211yesmaximal, characteristic, complemented
10#11729451C211yesmaximal, characteristic, complemented
11#11729450C211yesmaximal, characteristic, complemented
12#11729447C211yesmaximal, characteristic, complemented
13#11729446C211yesmaximal, characteristic, complemented
14#11729385C211yesmaximal, characteristic, complemented
15#11729381C211yesmaximal, characteristic, complemented
16C23×C7×Q8C2211yescharacteristic
17C23×C7×Q8C2211yescharacteristic
18C7×D4×Q8—24no—
19C7×D4×Q8C418yescomplemented
20C2×C7×C4⋊Q8—21no—
21C2×C7×C4⋊Q8C2211yescharacteristic
22C2×C7×C22⋊Q8—21no—
23C2×C7×C22⋊Q8—21no—
24C2×C7×C22⋊Q8C2211yescharacteristic
25C2×C7×C22⋊Q8C2211yescharacteristic
26C2×C4×C7×Q8C2211yescharacteristic
27C2×C4×C7×D4—21no—
28C2×C4×C7×D4C2211yescharacteristic
29C2×#6489C2211yescharacteristic
30C22×C4⋊Dic7C2211yescharacteristic
31C22×#1136C2211yescharacteristic
32C23×C7⋊C8C2211yescharacteristic
33#89997—24no—
34C2×#6409—24no—
35C2×#6409C2211yescharacteristic
36C2×#6409C2211yescharacteristic
37C2×#6409C2211yescharacteristic
38C2×#6409C2211yescharacteristic
39C2×#6409C2211yescharacteristic
40C2×#6409C2211yescharacteristic
41C2×#6409C2211yescharacteristic
42C2×#6409C2211yescharacteristic
43C2×#6409C2211yescharacteristic
44C2×#6409C2211yescharacteristic
45C2×#6409C2211yescharacteristic
46C2×#6409C2211yescharacteristic
47#89992—21no—
48#89984C2211yescharacteristic
49#89984C2211yescharacteristic
50C2×C22⋊(C7⋊C8)C2211yescharacteristic
51C2×C22⋊(C7⋊C8)C2211yescharacteristic
52#89783—24no—
53#89753—21no—
54#89723—21no—
55C22⋊C4×Dic7—21no—
56#89708C2211yescharacteristic
57C4×C4⋊Dic7C2211yescharacteristic
58C2×C4⋊(C7⋊C8)C2211yescharacteristic
59C2×#6377C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#89324C2211yescharacteristic
63#89324C2211yescharacteristic
64#22425—71nomaximal, Sylow
65C22×C7×Q8—21no—
66C22×C7×Q8—21no—
67C22×C7×Q8—22no—
68C22×C7×Q8—22no—
69C22×C7×Q8—22no—
70C22×C7×Q8—22no—
71C22×C7×Q8—22no—
72C22×C7×Q8—22no—
73C22×C7×Q8—41no—
74C22×C7×Q8—41no—
75C22×C7×Q8—41no—
76C22×C7×Q8—41no—
77C22×C7×Q8C2×C414yes—
78C22×C7×Q8C2×C414yescomplemented
79C22×C7×Q8C2311yescharacteristic
80C22×C7×Q8C2311yescharacteristic
81C22×C7×Q8C2311yescharacteristic
82C22×C7×D4D411yescharacteristic
83C23×C4×C7—21no—
84C23×C4×C7—21no—
85C23×C4×C7C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C23×Dic7—21no—
88C7×C4⋊Q8—28no—
89C7×C4⋊Q8—22no—
90C7×C4⋊Q8C2×C414yescomplemented
91C7×C22⋊Q8—22no—
92C7×C22⋊Q8—22no—
93C7×C22⋊Q8—28no—
94C7×C22⋊Q8—28no—
95C7×C22⋊Q8C2×C414yes—
96C7×C22⋊Q8C2×C414yescomplemented
97C4×C7×Q8—22no—
98C4×C7×Q8C2×C414yescomplemented
99C4×C7×D4—28no—
100C4×C7×D4C2×C414yes—
101C4×C7×D4D414yes—
102C2×C7×C4⋊C4—21no—
103C2×C7×C4⋊C4—21no—
104C2×C7×C4⋊C4—21no—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4D411yescharacteristic
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C22⋊C4—21no—
110C2×C7×C22⋊C4—21no—
111C2×C7×C22⋊C4D411yescharacteristic
112C2×C7×C22⋊C4D411yescharacteristic
113C2×C42×C7—21no—
114C2×C42×C7C2311yescharacteristic
115C2×C22⋊Dic7—21no—
116C2×C22⋊Dic7—21no—
117C2×C22⋊Dic7—21no—
118#6489—22no—
119#6489—41no—
120C2×C4⋊Dic7—22no—
121C2×C4⋊Dic7—21no—
122C2×C4⋊Dic7—41no—
123C2×C4⋊Dic7C2311yescharacteristic
124C2×C4⋊Dic7C2311yescharacteristic
125C2×C4⋊Dic7C2311yescharacteristic
126C2×C4⋊Dic7C2311yescharacteristic
127C2×C4×Dic7—21no—
128C2×C4×Dic7—21no—
129C2×#1136—22no—
130C2×#1136—22no—
131C2×#1136—41no—
132C22×C7⋊C8—22no—
133C22×C7⋊C8—22no—
134C22×C7⋊C8—41no—
135C22×C7⋊C8C2311yescharacteristic
136C22×C7⋊C8C2311yescharacteristic
137C22×C7⋊C8C2311yescharacteristic
138C22×C7⋊C8C2311yescharacteristic
139#6409—22no—
140#6409—22no—
141#6409—22no—
142#6409—22no—
143#6409—22no—
144#6409—22no—
145#6409—22no—
146#6409—41no—
147#6409—41no—
148#6409—41no—
149#6409—41no—
150#6409D414yescomplemented
151C7⋊#95—21no—
152C7⋊#95—21no—
153C7⋊#95—21no—
154C7⋊#95—21no—
155C7⋊#95—21no—
156C22⋊(C7⋊C8)—22no—
157C22⋊(C7⋊C8)—22no—
158C4⋊(C7⋊C8)—22no—
159#6377—22no—
160C2×D4×Q8D711yescharacteristic
161C2×#435—71no—
162C2×#419—71no—
163C22×#103—71no—
164#2352—71no—
165#1981—71no—
166#1960—71no—
167#1894—71no—
168#1892—71no—
169#1873—71no—
170#1872—71no—
171#1805—71no—
172#1787—71no—
173#1787—71no—
174#1763—71no—
175C24×C7C2×D411yescharacteristic
176C24×C7C2×D411yescharacteristic
177C2×C7×Q8—24no—
178C2×C7×Q8—24no—
179C2×C7×Q8—21no—
180C2×C7×Q8—21no—
181C2×C7×Q8—21no—
182C2×C7×Q8—21no—
183C2×C7×Q8—21no—
184C2×C7×Q8—28no—
185C2×C7×Q8—28no—
186C2×C7×Q8—21no—
187C2×C7×Q8—21no—
188C2×C7×Q8—21no—
189C2×C7×Q8—21no—
190C2×C7×Q8—21no—
191C2×C7×Q8—21no—
192C2×C7×Q8—21no—
193C2×C7×Q8—21no—
194C2×C7×Q8—42no—
195C2×C7×Q8—42no—
196C2×C7×Q8—42no—
197C2×C7×Q8—42no—
198C2×C7×Q8—44no—
199C2×C7×Q8—44no—
200C2×C7×Q8—44no—
201C2×C7×Q8—44no—
202C2×C7×Q8—44no—
203C2×C7×Q8—44no—
204C2×C7×Q8C22×C412yes—
205C2×C7×Q8C22×C412yes—
206C2×C7×Q8C22×C412yes—
207C2×C7×Q8C2×D412yes—
208C2×C7×Q8#4112yes—
209C2×C7×D4—22no—
210C2×C7×D4—22no—
211C2×C7×D4C22⋊C414yes—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—24no—
222C22×C4×C7—24no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—42no—
227C22×C4×C7—42no—
228C22×C4×C7—42no—
229C22×C4×C7—42no—
230C22×C4×C7C22×C412yes—
231C22×C4×C7C22×C412yes—
232C22×C4×C7C2×D411yescharacteristic
233C22×C4×C7C2×D411yescharacteristic
234C22×C4×C7C2×D411yescharacteristic
235C22×C4×C7C2×D411yescharacteristic
236C22×C4×C7C2×D412yes—
237C22×C4×C7C2×D412yes—
238C22×C4×C7C2411yescharacteristic
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7—21no—
242C22×Dic7—21no—
243C22×Dic7—42no—
244C22×Dic7—42no—
245C22×Dic7—81no—
246C7×C4⋊C4—24no—
247C7×C4⋊C4—24no—
248C7×C4⋊C4—24no—
249C7×C4⋊C4—24no—
250C7×C4⋊C4—24no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4C22⋊C414yes—
253C7×C4⋊C4C22×C412yes—
254C7×C22⋊C4—24no—
255C7×C22⋊C4—24no—
256C7×C22⋊C4C22⋊C414yes—
257C7×C22⋊C4C22⋊C414yes—
258C42×C7—24no—
259C42×C7C22×C412yes—
260C42×C7C2×D412yes—
261C22⋊Dic7—42no—
262C22⋊Dic7—42no—
263C22⋊Dic7—81no—
264C4⋊Dic7—21no—
265C4⋊Dic7—21no—
266C4⋊Dic7—21no—
267C4⋊Dic7—21no—
268C4⋊Dic7—21no—
269C4⋊Dic7—21no—
270C4⋊Dic7—21no—
271C4⋊Dic7—42no—
272C4⋊Dic7C2×D412yes—
273C4×Dic7—42no—
274C4×Dic7—81no—
275#1136—44no—
276C2×C7⋊C8—21no—
277C2×C7⋊C8—21no—
278C2×C7⋊C8—21no—
279C2×C7⋊C8—21no—
280C2×C7⋊C8—21no—
281C2×C7⋊C8—21no—
282C2×C7⋊C8—21no—
283C2×C7⋊C8—21no—
284C2×C7⋊C8—21no—
285C2×C7⋊C8—21no—
286C2×C7⋊C8—21no—
287C2×C7⋊C8—44no—
288C2×C7⋊C8C2×D412yes—
289C23×Q8C2×D711yescharacteristic
290C23×Q8C2×D711yescharacteristic
291C22×M16—71no—
292C23×C8—71no—
293D4×Q8—24no—
294D4×Q8Dic718yescomplemented
295C2×C4⋊Q8—21no—
296C2×C4⋊Q8C2×D711yescharacteristic
297C2×C22⋊Q8—21no—
298C2×C22⋊Q8—21no—
299C2×C22⋊Q8C2×D711yescharacteristic
300C2×C22⋊Q8C2×D711yescharacteristic
301C2×C4×Q8C2×D711yescharacteristic
302C2×C4×D4—21no—
303C2×C4×D4C2×D711yescharacteristic
304C2×#117—71no—
305C22×C4⋊C4—71no—
306#435—144no—
307C2×C4⋊C8—71no—
308#419—144no—
309C2×#103—71no—
310C2×#103—71no—
311C2×#103—71no—
312C2×#103—71no—
313C2×#103—71no—
314C2×#103—71no—
315C2×#103—71no—
316C2×#103—71no—
317C2×#103—71no—
318C2×#103—71no—
319C2×#103—71no—
320C2×#103—71no—
321C2×#103—144no—
322C2×C22⋊C8—71no—
323C2×C22⋊C8—71no—
324C2×#97—71no—
325#388—141no—
326#387—141no—
327#386—141no—
328#382—71no—
329#380—71no—
330#380—71no—
331C4×C4⋊C4—71no—
332C4×C22⋊C4—141no—
333#340—71no—
334#340—71no—
335#340—71no—
336#340—71no—
337C23×C7—21no—
338C23×C7—21no—
339C23×C7—21no—
340C23×C7—21no—
341C23×C7—21no—
342C23×C7—21no—
343C23×C7—21no—
344C23×C7—21no—
345C23×C7—21no—
346C23×C7—21no—
347C23×C7C2×C22⋊C412yes—
348C23×C7C2×C22⋊C412yes—
349C23×C7#13712yes—
350C23×C7#13712yes—
351C23×C7C22×D411yescharacteristic
352C7×Q8—22no—
353C7×Q8—22no—
354C7×Q8—22no—
355C7×Q8—22no—
356C7×Q8—22no—
357C7×Q8—22no—
358C7×Q8—22no—
359C7×Q8—48no—
360C7×Q8—48no—
361C7×Q8—41no—
362C7×Q8—41no—
363C7×Q8—41no—
364C7×Q8—41no—
365C7×Q8C4×D414yes—
366C7×D4—28no—
367C2×C4×C7—22no—
368C2×C4×C7—21no—
369C2×C4×C7—21no—
370C2×C4×C7—22no—
371C2×C4×C7—21no—
372C2×C4×C7—21no—
373C2×C4×C7—22no—
374C2×C4×C7—21no—
375C2×C4×C7—21no—
376C2×C4×C7—21no—
377C2×C4×C7—21no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—48no—
390C2×C4×C7—48no—
391C2×C4×C7—41no—
392C2×C4×C7—41no—
393C2×C4×C7—41no—
394C2×C4×C7—41no—
395C2×C4×C7—41no—
396C2×C4×C7—41no—
397C2×C4×C7C2×C22⋊C412yes—
398C2×C4×C7C2×C22⋊C412yes—
399C2×C4×C7C2×C22⋊C412yes—
400C2×C4×C7C2×C22⋊C412yes—
401C2×C4×C7C23×C411yescharacteristic
402C2×C4×C7C22×D411yescharacteristic
403C2×C4×C7C22×D411yescharacteristic
404C2×C4×C7C2×#4111yescharacteristic
405C2×C4×C7H(5,𝔽2)11yescharacteristic
406C2×C4×C7H(5,𝔽2)11yescharacteristic
407C2×Dic7—22no—
408C2×Dic7—41no—
409C2×Dic7—41no—
410C2×Dic7—41no—
411C2×Dic7—41no—
412C2×Dic7—41no—
413C2×Dic7—41no—
414C2×Dic7—41no—
415C2×Dic7—41no—
416C2×Dic7—41no—
417C2×Dic7—41no—
418C2×Dic7—41no—
419C2×Dic7—84no—
420C7⋊C8—22no—
421C7⋊C8—41no—
422C7⋊C8—41no—
423C7⋊C8—41no—
424C22×Q8—21no—
425C22×Q8—21no—
426C22×Q8—22no—
427C22×Q8—22no—
428C22×Q8—22no—
429C22×Q8—22no—
430C22×Q8—22no—
431C22×Q8—22no—
432C22×Q8—41no—
433C22×Q8—41no—
434C22×Q8—41no—
435C22×Q8—41no—
436C22×Q8C2×Dic714yes—
437C22×Q8C2×Dic714yescomplemented
438C22×Q8C22×D711yescharacteristic
439C22×Q8C22×D711yescharacteristic
440C22×Q8C22×D711yescharacteristic
441C22×D4C22⋊D711yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
444C23×C4—141no—
445C23×C4C22×D711yescharacteristic
446C23×C4C22×D711yescharacteristic
447C2×M16—142no—
448C2×M16—142no—
449C2×M16—281no—
450C22×C8—71no—
451C22×C8—71no—
452C22×C8—71no—
453C22×C8—71no—
454C22×C8—142no—
455C22×C8—142no—
456C22×C8—281no—
457C4⋊Q8—28no—
458C4⋊Q8—22no—
459C4⋊Q8C2×Dic714yescomplemented
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—28no—
463C22⋊Q8—28no—
464C22⋊Q8C2×Dic714yes—
465C22⋊Q8C2×Dic714yescomplemented
466C4×Q8—22no—
467C4×Q8C2×Dic714yescomplemented
468C4×D4—28no—
469C4×D4C2×Dic714yes—
470C4×D4C22⋊D714yes—
471#117—142no—
472#117—281no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—71no—
479C2×C4⋊C4—71no—
480C2×C4⋊C4—71no—
481C2×C4⋊C4—71no—
482C2×C4⋊C4—142no—
483C2×C4⋊C4—141no—
484C2×C4⋊C4—281no—
485C2×C4⋊C4C22⋊D711yescharacteristic
486C2×C4⋊C4C22×D711yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4C22⋊D711yescharacteristic
493C2×C22⋊C4C22⋊D711yescharacteristic
494C2×C42—21no—
495C2×C42—141no—
496C2×C42—141no—
497C2×C42C22×D711yescharacteristic
498C4⋊C8—142no—
499#103—74no—
500#103—142no—
501#103—142no—
502#103—142no—
503#103—142no—
504#103—142no—
505#103—142no—
506#103—142no—
507#103—281no—
508#103—281no—
509#103—281no—
510#103—281no—
511C22⋊C8—142no—
512C22⋊C8—142no—
513#97—142no—
514#95—141no—
515#95—141no—
516#95—141no—
517#95—141no—
518#95—141no—
519C22×C7—22no—
520C22×C7—22no—
521C22×C7—22no—
522C22×C7—22no—
523C22×C7—22no—
524C22×C7—22no—
525C22×C7—22no—
526C22×C7—22no—
527C22×C7—22no—
528C22×C7—41no—
529C22×C7—41no—
530C22×C7—41no—
531C22×C7—41no—
532C22×C7#41914yescomplemented
533C22×C7C22×C22⋊C411yescharacteristic
534C22×C7D4211yescharacteristic
535C22×C7#54611yescharacteristic
536C22×C7C2×#13711yescharacteristic
537C22×C7C2×#13711yescharacteristic
538C22×C7#57711yescharacteristic
539C22×C7#57811yescharacteristic
540C4×C7—22no—
541C4×C7—22no—
542C4×C7—24no—
543C4×C7—22no—
544C4×C7—22no—
545C4×C7—42no—
546C4×C7—42no—
547C4×C7—42no—
548C4×C7C2×C4×D411yescharacteristic
549C4×C7#51811yescharacteristic
550C4×C7D4211yescharacteristic
551C4×C7#54611yescharacteristic
552Dic7—42no—
553Dic7—81no—
554Dic7—81no—
555Dic7—81no—
556C24C2×C22⋊D711yescharacteristic
557C24C2×C22⋊D711yescharacteristic
558C2×Q8—24no—
559C2×Q8—24no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—28no—
566C2×Q8—28no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—42no—
576C2×Q8—42no—
577C2×Q8—42no—
578C2×Q8—42no—
579C2×Q8—44no—
580C2×Q8—44no—
581C2×Q8—44no—
582C2×Q8—44no—
583C2×Q8—44no—
584C2×Q8—44no—
585C2×Q8D4×D712yes—
586C2×Q8#115912yes—
587C2×Q8C22×Dic712yes—
588C2×Q8C22×Dic712yes—
589C2×Q8C22×Dic712yes—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4C22⋊Dic714yes—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—141no—
612C22×C4—141no—
613C22×C4—141no—
614C22×C4—141no—
615C22×C4—282no—
616C22×C4—282no—
617C22×C4—561no—
618C22×C4C22×Dic712yes—
619C22×C4C22×Dic712yes—
620C22×C4C2×C22⋊D711yescharacteristic
621C22×C4C2×C22⋊D711yescharacteristic
622C22×C4C2×C22⋊D711yescharacteristic
623C22×C4C2×C22⋊D711yescharacteristic
624C22×C4C2×C22⋊D712yes—
625C22×C4C2×C22⋊D712yes—
626C22×C4C23×D711yescharacteristic
627M16—284no—
628C2×C8—72no—
629C2×C8—141no—
630C2×C8—141no—
631C2×C8—141no—
632C2×C8—141no—
633C2×C8—141no—
634C2×C8—141no—
635C2×C8—141no—
636C2×C8—141no—
637C2×C8—141no—
638C2×C8—141no—
639C2×C8—141no—
640C2×C8—284no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—72no—
648C4⋊C4—141no—
649C4⋊C4—141no—
650C4⋊C4—141no—
651C4⋊C4—141no—
652C4⋊C4—141no—
653C4⋊C4—141no—
654C4⋊C4—141no—
655C4⋊C4—282no—
656C4⋊C4C22⋊Dic714yes—
657C4⋊C4C22×Dic712yes—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—282no—
661C22⋊C4—282no—
662C22⋊C4—561no—
663C22⋊C4C22⋊Dic714yes—
664C22⋊C4C22⋊Dic714yes—
665C42—24no—
666C42—282no—
667C42—561no—
668C42C22×Dic712yes—
669C42C2×C22⋊D712yes—
670C2×C7—24no—
671C2×C7—42no—
672C2×C7D4×C22⋊C411yescharacteristic
673C2×C7C2×#41911yescharacteristic
674C2×C7#289811yescharacteristic
675C2×C7#326611yescharacteristic
676C2×C7#327011yescharacteristic
677C2×C7#331211yescharacteristic
678C2×C7#332011yescharacteristic
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23#650512yes—
690C23#650512yes—
691C23C2×C22⋊Dic712yes—
692C23C2×C22⋊Dic712yes—
693C23C22×C22⋊D711yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8—22no—
701Q8—48no—
702Q8—48no—
703Q8—41no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707Q8D4×Dic714yes—
708D4—28no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—48no—
732C2×C4—48no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—142no—
740C2×C4—281no—
741C2×C4—281no—
742C2×C4—281no—
743C2×C4—281no—
744C2×C4—281no—
745C2×C4—281no—
746C2×C4—281no—
747C2×C4—281no—
748C2×C4—281no—
749C2×C4—281no—
750C2×C4—281no—
751C2×C4—564no—
752C2×C4C2×C22⋊Dic712yes—
753C2×C4C2×C22⋊Dic712yes—
754C2×C4C2×C22⋊Dic712yes—
755C2×C4C2×C22⋊Dic712yes—
756C2×C4C2×D4×D711yescharacteristic
757C2×C4C2×#115911yescharacteristic
758C2×C4#654811yescharacteristic
759C2×C4#654811yescharacteristic
760C2×C4C23×Dic711yescharacteristic
761C2×C4C22×C22⋊D711yescharacteristic
762C8—142no—
763C8—281no—
764C8—281no—
765C8—281no—
766C7#2242511yescharacteristic, complemented, Sylow
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22#8999714yescomplemented
781C22D4×C22⋊D711yescharacteristic
782C22#9049711yescharacteristic
783C22C2×#650511yescharacteristic
784C22C2×#650511yescharacteristic
785C22#9052811yescharacteristic
786C22#9052911yescharacteristic
787C22C22×C22⋊Dic711yescharacteristic
788C4—22no—
789C4—22no—
790C4—24no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—282no—
797C4—561no—
798C4—561no—
799C4—561no—
800C4C2×D4×Dic711yescharacteristic
801C4#9048911yescharacteristic
802C4D4×C22⋊D711yescharacteristic
803C4#9049711yescharacteristic
804C2—24no—
805C2—42no—
806C2#1174099711yescharacteristic
807C2#1174099811yescharacteristic
808C2#1174100411yescharacteristic
809C2#1174101011yescharacteristic
810C2D4×C22⋊Dic711yescharacteristic
811C2C2×#8999711yescharacteristic
812C2#1174155611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×D4×Q8C2
socleC23×C7C22×D4
prime radicalC22×C7×D4D4
cosocleC22×C4×C7C24
hypercenterC2×D4×Q8D7
hypocenterC7#22425
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#89997C2semidirect
3. C22×#6409C2semidirect
6. #11729886C2semidirect
7. #11729886C2semidirect
8. #11729540C2semidirect
9. #11729532C2semidirect
10. #11729451C2semidirect
11. #11729450C2semidirect
12. #11729447C2semidirect
13. #11729446C2semidirect
14. #11729385C2semidirect
15. #11729381C2semidirect
19. C7×D4×Q8C4semidirect
78. C22×C7×Q8C2×C4semidirect
90. C7×C4⋊Q8C2×C4semidirect
96. C7×C22⋊Q8C2×C4semidirect
98. C4×C7×Q8C2×C4semidirect
150. #6409D4semidirect
294. D4×Q8Dic7semidirect
437. C22×Q8C2×Dic7semidirect
459. C4⋊Q8C2×Dic7semidirect
465. C22⋊Q8C2×Dic7semidirect
467. C4×Q8C2×Dic7semidirect
532. C22×C7#419semidirect
766. C7#22425semidirect
780. C22#89997semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C7×D4×Q82
C2×#899972
C22×#64092
#117397802
C2×#897832
#117298862
#117295402
#117295322
#117294512
#117294502
#117294472
#117294462
#117293852
#117293812
#224257